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摘要: 为了降低高速公路养护成本, 运用边际成本管理原理, 建立高速公路交通流量、道路长度与养护成本之间的多元回归分析数学模型, 针对预防养护和专项工程养护方式, 运用统计方法, 推导了各项因素的边际成本表达式, 提出高速公路养护作业成本的预测模型及成本管理的边际成本和弹性指数的概念, 计算了交通流量、道路长度与养护成本相关的弹性指数, 分析了与交通流量相关的高速公路养护费用经济指标。计算结果表明: 交通流量和高速公路长度对养护维修成本起决定作用, 维修费用随交通流量和道路长度成对数关系变化, 而高速公路养护维修平均费用随着交通流量增加而降低。Abstract: In order to decrease expressway maintenance cost, the mathematic model between maintenance cost and the factors of traffic flow and road length was established by using the management theory of marginal cost, aimed at preventive maintenance and special project maintenance for asphalt pavement on expressway, the marginal cost expression of every factor was derived by using statistical method, the concepts of marginal cost of expressway maintenance management and maintenance elastic index were first expressed, and a forecast model of expressway maintenance cost was established. With the model, the elastic indices of traffic flow and road length relating to maintenance cost were calculated, and the economic indices of expressway maintenance cost relating to traffic flow were analyzed. Computation result shows that traffic flow and road length are the primary influence factors on expressway maintenance cost, there is logarithmic change relationship between road length and expressway maintenance cost, and expressway maintenance average cost decreases with traffic flow increase.
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Key words:
- road engineering /
- expressway /
- maintenance cost /
- cost forecast model
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图 4 交通流量与平均养护费用和边际成本的关系
Figure 4. Relation between traffic flow, average maintenance cost and marginal cost
表 1 高速公路A数据平均值
Table 1. Average values of expressway A data
变量 年份 2001 2002 2003 维修费用/万元 258.8 255.5 251.8 维修道路长度/km 66.68 66.32 66.23 匝道数 5.0 4.0 3.0 桥梁数 5.0 5.0 5.0 路面质量指标 2.18 2.41 2.65 预防养护 0.33 0.33 0.34 利用程度(自然对数) 14.92 14.79 14.78 
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表 2 高速公路B数据平均值
Table 2. Average values of expressway B data
变量 年份 2001 2002 2003 维修费用/万元 233.0 230.6 229.5 再投资费用/万元 311.0 311.8 329.8 维修道路长度/km 80.63 80.62 81.22 匝道数 4.0 4.0 4.0 桥梁数 5.0 5.0 6.0 专项工程 0.57 0.57 0.52 利用程度(自然对数) 14.06 14.59 1.83
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表 3 统计参数
Table 3. Statistical parameters
变量 A模型 B模型 数值 t分布 数值 t分布 α -6.749 -3.924 -6.828 -4.210 α95 -0.005 -0.093 0.000 0.003 α96 0.013 0.241 0.005 0.292 I/βi 0.026 0.342 0.004 0.048 y/βy* 2.338 5.943 2.023 5.589 u/βu* 0.986 5.051 1.037 5.692 yu/βyu -0.104 -5.868 -0.096 -5.665 y2/βyy -0.010 -0.294 0.023 0.786 u2/βuu -0.014 -2.288 -0.017 -2.995 桥梁数 0.005 0.708 — — 匝道数 0.011 3.601 0.010 3.462 匝道数平方/100 0.006 1.184 0.005 1.169 模型成本变动指数 0.210 2.290 0.269 3.022 相关系数 — 0.767 — 0.736
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表 4 预防养护和专项工程的统计参数
Table 4. Statistical parameters of preventive maintenance and special project
变量 预防养护费用 专项工程费用 数学期望 t分布 数学期望 t分布 α 8.780 6.645 10.764 2.967 α98 -0.104 -2.145 -0.036 -0.269 α99 -0.139 -2.830 -0.051 -0.381 I/βI -0.318 -4.936 -0.550 -3.102 y/βy* 1.504 3.462 1.408 1.179 u/βu* 0.167 1.501 0.336 1.065 yu/βyu 0.001 0.071 -0.018 -0.341 y2/βyy -0.104 -2.766 -0.078 -0.754 u2/βuu -0.006 -1.519 0.026 2.234 匝道数 0.010 4.460 0.012 1.889 速度 0.013 3.298 0.005 0.478 相关系数 — 0.827 — 0.498
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